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Knot invariants and Hecke correspondences
by
Ben Webster
University of Virginia
The Jones polynomial and other Reshetikhin-Turaev invariants are blessed (or depending on your perspective, cursed) with two complementary and quite different descriptions: Witten has written them as expectation values for Wilson loop operators in Chern-Simons theory, but in order to effectively compute them, we can exploit dimensional reduction which gives us a description in terms of very simple tangles (using quantum groups).
Much more recently, Witten has proposed a similar approach to understanding Khovanov homology using field theories (essentially the counting of solutions to PDEs). I'll try to give a mathematician's perspective on this theory, and the dimensional reduction approach to computing it. Just as quantum groups spring fully formed from the forehead of Chern-Simons theory, this approach gives us another perspective to understand the constructions of homological knot invariants, including KLR algebras.
Date received: April 17, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbof-13.